Year: 2026
Type: article
Abstract: . Wilson–Cowan and Amari-type models describe the nonlinear dynamics of interacting neural populations, providing a fundamental framework for modeling how sensory and other exogenous inputs shape neural activity. This article investigates the controllability properties of Amari-type neural field equations subject to piecewise constant-in-time and constant-in-time inputs. The model describes the time evolution of polarization in neural tissue within a spatial continuum, with synaptic interactions modeled by a convolution kernel. We study the synthesis of constant-in-time and piecewise constant-in-time inputs to achieve two-point boundary-type control objectives, namely, steering neural activity from an initial state to a prescribed target state. This approach is particularly relevant for predicting the emergence of paradoxical neural representations, such as discordant visual illusions elicited by overt sensory stimuli. We first present a control synthesis based on the Banach fixed-point theorem, yielding an iterative construction of a constant-in-time input under minimal regularity assumptions on the kernel and transfer function; however, it has practical limitations, even in the linear case. To overcome these challenges, we then develop a generic synthesis framework based on the flow of neural dynamics drift, enabling explicit piecewise constant and constant-in-time inputs. Extensive numerical results in one and two spatial dimensions confirm the effectiveness of the proposed syntheses and show that they consistently outperform inputs derived from naive linearization at the initial or target states when these states are not equilibria of the drift dynamics. By providing a mathematically rigorous framework for controlling delay-free Amari-type neural fields, this work advances our understanding of nonlinear neural population control with potential applications in computational neuroscience, psychophysics, and neurostimulation.
DOI: 10.1137/24m1719979
Authors: Cyprien Tamekue, ShiNung Ching
Institution: Washington University in St. Louis
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Institutes of Health
OpenAlex ID: W7165758460